Libraries and utility functions

import pandas as pd
import numpy as np
import seaborn as sns
sns.set_style("whitegrid")
from sklearn.preprocessing import MinMaxScaler
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error

Load data

df = pd.read_csv('datasets/california_housing_train.csv')
df.head()

	longitude	latitude	housing_median_age	total_rooms	total_bedrooms	population	households	median_income	median_house_value
0	-114.31	34.19	15.0	5612.0	1283.0	1015.0	472.0	1.4936	66900.0
1	-114.47	34.40	19.0	7650.0	1901.0	1129.0	463.0	1.8200	80100.0
2	-114.56	33.69	17.0	720.0	174.0	333.0	117.0	1.6509	85700.0
3	-114.57	33.64	14.0	1501.0	337.0	515.0	226.0	3.1917	73400.0
4	-114.57	33.57	20.0	1454.0	326.0	624.0	262.0	1.9250	65500.0

Exploratory Data Analysis (EDA)

Distribution of the features

Joint Plots

for col1 in df.columns.to_list():
    for col2 in df.columns.to_list():
        if col1 != col2:
            sns.jointplot(data=df, x=col1, y= col2)

d:\projects\pycharmprojects\ml_2021\venv2\lib\site-packages\seaborn\axisgrid.py:1598: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).
  f = plt.figure(figsize=(height, height))

Violin-plots

ax = sns.violinplot(data=df, x="longitude")

ax = sns.violinplot(data=df, x="latitude")

ax = sns.violinplot(data=df, x="housing_median_age")

ax = sns.violinplot(data=df, x="total_rooms")

ax = sns.violinplot(data=df, x="total_bedrooms")

ax = sns.violinplot(data=df, x="population")

ax = sns.violinplot(data=df, x="households")

ax = sns.violinplot(data=df, x="median_income")

ax = sns.violinplot(data=df, x="median_house_value")

Pair Plots

sns.pairplot(df)

<seaborn.axisgrid.PairGrid at 0x1a5909bd5b0>

Between feature dependance

ax = sns.heatmap(df.corr(), linewidths=.5)

Data pre-processing

Features and target split

X = df.drop(columns=["median_house_value"])
y = df['median_house_value']

Normalization

scaler = MinMaxScaler()
X = scaler.fit_transform(X)

Train-test split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20)

Linear Regression Model

Model Training

regressor = LinearRegression()

regressor.fit(X_train, y_train)

LinearRegression()

Model Evaluation

y_pred = regressor.predict(X_test)

'Mean Squared Error: 4795883823.951487'

print(f'Mean Squared Error: {mean_squared_error(y_test, y_pred)}')
print(f"Coefficients W = {regressor.coef_}")
print(f"Intercept W_0 = {regressor.intercept_}")

Mean Squared Error: 4795883823.951487
Coefficients W = [ -433775.5900699   -405629.64501937    54401.20493929  -304240.57793445
   685837.50476176 -1347415.24445914   319816.61761417   579299.89968707]
Intercept W_0 = 373877.65779367456